Unified Signal Theory
Unified Signal Theory is an indispensible textbook dealing with the theory of deterministic signals; a topic of fundamental interest to graduates and senior undergraduates in the areas of information engineering (telecommunications, control, systems theor
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Gianfranco Cariolaro
Unified Signal Theory
Gianfranco Cariolaro University of Padova Padova, Italy [email protected]
ISBN 978-0-85729-463-0 e-ISBN 978-0-85729-464-7 DOI 10.1007/978-0-85729-464-7 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Mathematics Subject Classification (2010): 94A12, 22D35, 28C10, 43A25, 47A20, 46C15 © Springer-Verlag London Limited 2011 Matlab® and Simulink® are registered trademarks of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA. http://www.mathworks.com Mathematica® is a registered trademark of Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237, USA. http://www.wolfram.com Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
e pluribus unum
To my son David
Foreword
Methodological reductionism is a driving force of scientific thinking. Unlike the more controversial, and philosophically dubious, connotations of the term, methodological reductionism embodies a general principle of intellectual parsimony. It does not establish debatable hierarchies among pedagogically distinct scientific areas, it does not seek to identify equally controversial ultimate constituents of reality. Instead, it attempts the consolidation of a collection of more or less intuitively connected items into a more general item, of which they become refinements or specializations. This trend towards simplicity (the parsimony of explanation) is the underlying fabric of scientific endeavor. Simplicity is the hallmark of that undefinable quality of science called “elegance”: a simpler proof of a theorem is unmistakably referred to as “more elegant” than a previous more cumbersome proof of the same statement. The incorporation of the descriptive results of Kepler and Galileo into the mechanics of Newton is a major example. Equally spectacular is the unification of a number of relations concerning elect
